1. Field of the Invention
This invention relates, generally, to security measures for wireless transmissions. More particularly, it relates to methods for preventing synchronization to a transmitted signal by an unauthorized user.
2. Description of the Prior Art
Orthogonal frequency division multiplexing (OFDM) systems exhibit immunity to multipath distortion. In OFDM, the linear convolution of a transmitted signal with a channel impulse response (CIR) is converted to circular convolution by cyclically extending the transmitted OFDM symbols. The transmitted data symbols are recovered using a simple one-tap equalizer in the frequency domain. The redundancy introduced by cyclic prefix (CP) can be used for channel estimation and synchronization as well. However. CP may be undesirable for covert applications because unauthorized users may explore the periodicity introduced by the CP to synchronize to the transmitted signal.
To remove the distortion due to multipath, the length of the CP should be larger than the maximum excess delay of the channel. When the length of the CP is smaller than the maximum excess delay, previously transmitted OFDM symbols interfere with a current OFDM symbol as indicated in FIG. 1 (prior art). This type of interference is known as inter-symbol interference (ISI) or interblock interference (IBI) and the performance degradation due to ISI is investigated in equations [1] and [2] below. The power spectral density of the interference is derived in terms of the CIR and the CP length in equation [1]. Assuming there are only post-cursors from the preceding symbol, the signal-to-noise ratio (SNR) of the received signal at each subcarrier position can be written as:
                              SNR          ⁡                      (            k            )                          =                              1            2                    ⁢                                                                                                            H                    ⁡                                          (                      k                      )                                                                                        2                            ⁢              N                                                      ∑                n                L                            ⁢                                                          ⁢                                                N                                      CP                    +                    1                                                  ⁢                                                                                                h                      n                                                                            2                                                                                        (        1        )            
Where H(k) is the channel frequency response (CFR) at kth subcarrier, N is the fast Fourier transform (FFT) size, h is the nth tap of CIR, and L is the length of the CIR.
As indicated by equation (1), the degradation depends on the ratio between the tail power of the CIR and total power of CIR, as indicated in FIG. 2 (prior art), which shows BER degradation as a function of guard interval length in a noiseless environment. The length of the power delay profile (PDP) is denoted 20 and it is assumed to be exponentially decaying. Calculating the SNR in each sub-carrier and calculating the average BER provides theoretical results. As FIG. 2 shows, insufficient CP length causes irreducible error floor in OFDM.
The redundancy introduced by the CP can be used to estimate time and frequency offsets. Synchronization algorithms based on the maximum likelihood (ML), equation [3], minimum mean-square error (MMSE), equation [4], and the maximum correlation (MC), equation [5] criteria use the periodicity introduced by the cyclic prefix to estimate the timing and frequency offsets.
The ML method is illustrated in FIG. 3 where only one OFDM symbol is shown. The synchronization metric obtained by one OFDM symbol can be written as
                              M          ⁡                      (            m            )                          =                              ∑                          n              =              0                                                      N                CP                            -              1                                ⁢                                          ⁢                                    r              ⁡                              (                                  m                  -                  n                                )                                      ⁢            r            *                          (                              m                -                n                +                                  N                  D                                            )                                                          (        2        )            
where r(n) is the received signal, NCP is the length of CP and ND is the length of the useful data part. Using (2), the timing position can be found as{circumflex over (T)}n=arg max|M(m)|  (3)
and frequency offset estimation as
                              ɛ          ^                =                              1                          2              ⁢              π                                ⁢          ∠          ⁢                                          ⁢                      M            ⁡                          (                                                T                  ^                                n                            )                                                          (        4        )            
These estimates should be averaged over different OFDM symbols to obtain reliable estimates. Adding the correlation metrics from different symbols and dividing by the number of symbols provides the needed average. As the number of available OFDM symbols increase, the estimates become more accurate. The resulting synchronization metric and the final metric obtained by averaging are shown in FIG. 5 (prior art) where the effect of averaging is depicted.
The respective lengths of the OFDM symbol and CP can be estimated blindly by exhaustive searching. This knowledge gives undesired or unauthorized users the ability to synchronize to the transmitted signal. FIG. 4 (prior art) shows the magnitude of the synchronization metric as a function of different CP and OFDM symbol sizes. As indicated in FIG. 4, the peak occurs when the hypothesized lengths are equal to the correct lengths.
The periodicity inherently introduced by the usage of CP can be explored by undesired users to synchronize to the transmitted signal.
Accordingly, what is needed in the art is a technique that prevents unauthorized synchronization while maintaining the advantages of the CP.
However, in view of the prior art considered as a whole at the time the present invention was made, it was not obvious to those of ordinary skill in this art how the needed additional security could be provided.